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Chemical Engineering Science, Vol.58, No.15, 3303-3326, 2003
Nanofiltration modeling: the role of dielectric exclusion in membrane characterization
A general model is presented, called Donnan steric pore model & dielectric exclusion (DSPM&DE) to describe mass transfer of electrolytes and neutral solutes through nanofiltration membranes. The transport equations of ions through the membrane are based on the extended Nernst-Planck equation, accounting for ionic diffusion, electromigration and convection in the membrane pores; the hindered nature of diffusion and convection of the species inside the membrane is considered. Ionic partitioning at the interfaces between the membrane and the external phases takes into account of three separation mechanisms: steric hindrance, Donnan equilibrium and dielectric exclusion. The role of the difference existing between the dielectric constant of the aqueous solution in the pores and the dielectric constant of the membrane material is assumed dominant in determining the rejection mechanism related to the dielectric effects. The membrane is characterized through the use of adjustable parameters such as the average pore radius, the effective membrane thickness and the volumetric charge density.A general assessment is presented for membrane characterization. A new procedure is introduced for the membrane parameters calculation, based on a simple analytical relationship developed to describe rejection of single symmetric electrolytes.Two versions of the DSPM&DE model are presented, in which the "integral" model is a weak simplification of the general "differential" model. The validity of the models presented is fully demonstrated in the case of negatively charged membranes, through the comparison with experimental results performed in a wide range of operative conditions. The separation effect related to the dielectric exclusion is relevant with respect to Donnan equilibrium in determining bivalent counter-ions rejection, such as CaCl2 as well as MgSO4, whereas dielectric effects are not so remarkable in the case of mixtures containing various co-ions, such as NaCl + Na2SO4. (C) 2003 Elsevier Ltd. All rights reserved.
Keywords:membranes;mathematical modeling;nanofiltration;electrolytes;dielectric exclusion;membrane characterization